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RATIONAL INVARIANTS OF CERTAIN ORTHOGONAL AND UNITARY GROUPS D. CARLISLE AND P. H. KROPHOLLER The purpose of this note is to prove a conjecture of Huah Chu [1] on modular rational invariants of finite orthogonal groups. In an appendix we briefly describe how similar results can be proved for unitary groups. Recently, in [2], S. D. Cohen established a special case of Huah Chu's conjecture, and here we adopt Cohen's notation. Thus q is an odd prime power, n is a positive integer, V = F£ is an n- dimensional vector space over ¥ = GF{q) and Q (x ...,x ) is a non-degenerate g n lt n quadratic form on V. Without loss of generality we may assume that X X = X Qn( l> • • •' n) iLjA-K k> where the A eF are non-zero. Here we write fc ff P -IV J Y A A ''O ~~ 2 La fc *> and for i; ^ 1, In the notation of [2] we have Q (i) = £,/2 for i ^ 1 and Q (0) = £ . As in [2], we write n n 0 K for the field F (x ... , x )
Bulletin of the London Mathematical Society – Wiley
Published: Jan 1, 1992
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